Selection of superior soybean genotypes across locations and years in Zimbabwe according to multitrait ideotype
Introduction
Question
How to select superior soybean genotypes across locations and years (GxE interaction) according to Multitrait ideotype? (Simultaneous selection)
Hypothesis
Estimate probability of superior performance (Dias et al. 2022) across locations and years and classify genotypes using Bayesian Probabilistic Selection Index (Chagas et al. 2025)
Goal
Important
Select superior soybean genotypes to grain yield, plant height and plant lodging using Bayesian probabilistic selection index (BPSI) (Chagas et al. 2025)
Material and Methods
- 14 locations
- 6 years
- 41 trials
- 98 genotypes
- 3 traits (Grain Yield, Plant Height, Plant Lodging)
- Randomized complete block design (RCB)
- Using package ProbBreed (Chaves et al. 2024)
Material and Methods
Individual analyses
\[ \mathbf{y} = \mathbf{X_1b} + \mathbf{Z_1g} + \mathbf{\epsilon} \]
where \(\mathbf{y}\) is the vector of phenotypic observations, \(\mathbf{b}\) is the vector of fixed effects of replication, \(\mathbf{g}\) is the vector of random effects of genotypes and \(\mathbf{\epsilon}\) is the vector of random errors. \(\mathbf{X_1}\), \(\mathbf{X_2}\) e \(\mathbf{Z_1}\) are incidence matrix of \(\mathbf{b}\) and \(\mathbf{g}\) effects respectively..
Material and Methods
Heritability
\[ h^2 = \sigma^2g / \sigma^2g + \sigma^2e \]
where \(\sigma^2g\) is the genetic variance and \(\sigma_e^2\) is the residual variance.
Experimental Coeficient of Variation
\[ CV = \frac{\sigma_e}{\mu} \times 100 \]
where \(\mu\) is the trait mean.
Material e Métodos
Likelihood ratio test
\[LRT= −2 \times (Log𝐿 - Log L_𝑅)\]
where \(L\) is the maximum point of residual likelihood function of the complete model and \(L_R\) is the same for the reduced model, that is, without the effect to be tested. The LRT value was compared with a tabulated value based on the chi-square table, with one degree of freedom and 0.95 probability.
Material and Methods
Bayesian model
\[ y_{jkhp} = \mu + t_h + l_k + b_{p(k)} + g_j + gl_{jk} + gt_{jh} + \varepsilon_{jkhp} \] where the \(y_{jkhp}\) is the phenotypic record of the \(j^{th}\) genotype, allocated in the \(p^{th}\) block, in the \(k^{th}\) location and in the year \(t_{th}\). All other effects were previously defined but \(b_{p(k)}\), which is the effect of the \(p^{th}\) block in the \(k{th}\) location, and \(gl^{jk}\) , which correspond to the genotype-by-location interaction \(t_h\) and \(t_{jh}\) are the main effect of years and the genotypes-by-years interaction effect, respectively.
Material and Methods
Probability of superior performance
BPSI index uses the probability of superior performance to estimate the chance of a genotype being selected in multienvironmental trials (Dias et al. 2022).
\[ Pr\left({\hat{g}}_i \in \Omega \middle| y\right) = \frac{1}{s}\sum_{s=1}^{s} I \left({\hat{g}}_i^{(s)} \in \Omega \middle| y\right) \]
where \(\hat{g}_i\) is the genotypic value, \(\Omega\) is a subset of genotypes with superior performance and \(s\) represents each sample of posterior distribution.
Material and methods
Bayesian Probabilistic Selection Index
\[ BPSI_i = \sum_{m=1}^{t} \frac{RankProbSup^t}{\omega^t} \]
where \(t\) is the total number of traits evaluated \((m =1, 2,…,t)\) and \(\omega\) is a weight. Traits of greater interest will have larger \(\omega\). We used weight 2 for GY and weight 1 for PH and PL. The 10% best-ranked families were selected according to the BPSI.
| Genotype | T1(Rank) | T2(Rank) | T3(Rank) | PSI |
|---|---|---|---|---|
| 1 | 10 | 5 | 2 | ∑ i.= 17 |
| 2 | 5 | 3 | 10 | ∑ i.= 18 |
| 3 | 7 | 3 | 10 | ∑ i.= 19 |
Results
Results
Results
Results
Results
Results
Results
Variances
Results
Variances
Results
Density
Results
Within
Results
Across
Results
Density
BPSI
load("../Saves/res_PL_year.rda")
load("../Saves/res_PH_year.rda")
load("../Saves/res_GY_year.rda")
source("../data/bpsi_fun.R")
models= vector("list",length(3))
models[[1]] = res_GY;
models[[2]] = res_PH
models[[3]] = res_PL
models[[3]]$across$perfo <- models[[3]]$across$perfo[-which(models[[3]]$across$perfo$ID=="G_55"),]
names(models) <- c("GY","PH","PL")
BPSI_soy=BPSI(modlist = models,increase =c(TRUE,FALSE,FALSE),omega = c(2,1,1),int = 0.1,save.df = T,verbose = T )
df=print(BPSI_soy) GY PH PL bpsi sel gen
1 0.5 4.0 4.0 8.5 selected G_20
2 8.0 6.0 4.0 18.0 selected G_3
3 3.0 2.0 17.5 22.5 selected G_38
4 7.0 5.0 18.0 30.0 selected G_45
5 13.0 3.0 15.0 31.0 selected G_4
6 7.0 8.0 24.5 39.5 selected G_13
7 29.0 12.0 5.0 46.0 selected G_16
8 19.0 18.0 14.0 51.0 selected G_1
9 2.0 49.0 1.5 52.5 selected G_32
10 19.0 21.5 12.0 52.5 selected G_33
11 27.0 7.0 19.0 53.0 not_sel G_14
12 15.0 38.0 4.5 57.5 not_sel G_21
13 10.0 17.0 33.0 60.0 not_sel G_31
14 57.0 1.0 2.5 60.5 not_sel G_54
15 2.0 52.0 7.0 61.0 not_sel G_50
16 17.0 17.5 28.0 62.5 not_sel G_28
17 48.0 3.5 11.0 62.5 not_sel G_64
18 5.0 47.0 13.0 65.0 not_sel G_93
19 13.0 42.0 13.5 68.5 not_sel G_40
20 34.0 24.0 11.5 69.5 not_sel G_49
21 23.0 25.0 23.0 71.0 not_sel G_60
22 37.0 18.0 17.0 72.0 not_sel G_39
23 20.5 39.0 13.0 72.5 not_sel G_68
24 36.0 29.0 8.0 73.0 not_sel G_8
25 24.0 34.0 18.5 76.5 not_sel G_77
26 3.0 61.0 20.0 84.0 not_sel G_53
27 18.0 24.0 47.0 89.0 not_sel G_36
28 21.0 38.0 30.0 89.0 not_sel G_47
29 33.0 20.5 38.0 91.5 not_sel G_52
30 23.0 30.0 39.0 92.0 not_sel G_29
31 9.0 28.0 55.0 92.0 not_sel G_44
32 14.0 76.0 2.0 92.0 not_sel G_9
33 32.0 9.5 51.0 92.5 not_sel G_11
34 43.0 28.0 21.5 92.5 not_sel G_74
35 11.0 58.0 25.0 94.0 not_sel G_42
36 44.0 13.0 43.5 100.5 not_sel G_58
37 12.0 36.0 53.0 101.0 not_sel G_25
38 73.0 10.0 24.0 107.0 not_sel G_67
39 11.0 76.0 20.5 107.5 not_sel G_46
40 68.0 23.0 18.0 109.0 not_sel G_10
41 55.0 4.5 50.0 109.5 not_sel G_2
42 49.0 16.0 45.0 110.0 not_sel G_30
43 77.0 13.0 21.0 111.0 not_sel G_75
44 15.0 53.0 44.0 112.0 not_sel G_92
45 54.0 5.0 54.0 113.0 not_sel G_17
46 10.0 76.0 29.5 115.5 not_sel G_43
47 81.0 5.5 29.0 115.5 not_sel G_5
48 31.0 25.0 60.0 116.0 not_sel G_89
49 33.5 22.0 63.0 118.5 not_sel G_6
50 65.0 15.0 40.0 120.0 not_sel G_88
51 8.0 76.0 40.0 124.0 not_sel G_34
52 30.5 72.0 22.0 124.5 not_sel G_70
53 35.0 76.0 16.0 127.0 not_sel G_63
54 51.0 76.0 0.5 127.5 not_sel G_27
55 47.0 15.5 66.0 128.5 not_sel G_94
56 45.0 60.0 24.0 129.0 not_sel G_35
57 50.0 76.0 3.0 129.0 not_sel G_51
58 20.0 76.0 34.0 130.0 not_sel G_26
59 59.0 22.5 52.0 133.5 not_sel G_61
60 42.0 38.0 57.0 137.0 not_sel G_91
61 39.0 38.0 64.0 141.0 not_sel G_41
62 86.0 16.0 41.0 143.0 not_sel G_19
63 31.0 40.0 76.0 147.0 not_sel G_84
64 80.0 27.0 42.0 149.0 not_sel G_97
65 32.0 27.0 90.0 149.0 not_sel G_98
66 63.0 23.0 65.0 151.0 not_sel G_72
67 38.5 21.0 93.0 152.5 not_sel G_65
68 33.0 59.0 62.0 154.0 not_sel G_81
69 56.0 64.0 35.0 155.0 not_sel G_85
70 12.5 76.0 67.0 155.5 not_sel G_73
71 58.0 64.0 39.5 161.5 not_sel G_82
72 60.0 64.0 41.0 165.0 not_sel G_90
73 35.5 72.0 58.0 165.5 not_sel G_48
74 40.5 33.0 93.0 166.5 not_sel G_57
75 43.0 69.0 56.0 168.0 not_sel G_87
76 26.0 55.0 88.0 169.0 not_sel G_76
77 53.0 28.5 89.0 170.5 not_sel G_80
78 42.0 64.0 68.0 174.0 not_sel G_12
79 34.5 62.0 84.0 180.5 not_sel G_95
80 90.0 76.0 15.5 181.5 not_sel G_24
81 37.5 70.0 75.0 182.5 not_sel G_18
82 84.0 38.0 61.0 183.0 not_sel G_22
83 86.0 63.0 35.5 184.5 not_sel G_71
84 86.0 25.5 73.0 184.5 not_sel G_83
85 70.0 38.0 77.0 185.0 not_sel G_78
86 79.0 18.5 90.0 187.5 not_sel G_56
87 74.0 70.0 45.0 189.0 not_sel G_96
88 81.0 76.0 36.0 193.0 not_sel G_66
89 90.0 22.0 81.0 193.0 not_sel G_7
90 72.0 36.0 86.0 194.0 not_sel G_86
91 45.0 76.0 74.0 195.0 not_sel G_23
92 90.0 38.0 69.0 197.0 not_sel G_59
93 45.0 76.0 78.0 199.0 not_sel G_37
94 38.0 76.0 85.0 199.0 not_sel G_79
95 45.0 64.0 93.0 202.0 not_sel G_15
96 90.0 76.0 46.5 212.5 not_sel G_69
97 45.0 76.0 93.0 214.0 not_sel G_62Results
Highlighting the ranking of probability of superior performance per trait of the selected families.
Figure 1: Ranking of probability of superior performance per trait
Results
Figure 2: Selected families based on BPSI rank
Title?
- Selection of superior soybean genotypes across locations and years in Zimbabwe according to multitrait ideotype
- Multitrait selection of soybean varieties using Bayesian probabilistic selection index
- josetchagas@usp.br
- Obrigado!
Referências
DGM Lab